熵垒是导致经典和量子算法困难的原因
Entropic barriers as a reason for hardness in both classical and quantum algorithms
摘要：
我们研究了经典和量子算法来解决一个困难的优化问题，即3-XORSAT 3-正则随机图。通过引入一个新的准贪婪算法，不允许跳过大的能量障碍，我们表明，问题的硬度主要是由于熵障碍。我们研究，分析和数值计算，几种优化算法，发现熵障碍以类似的方式影响经典的本地算法和量子退火。对于绝热算法，我们确定的困难是不同的隧道下的大障碍，但尽管如此，引起指数运行（退火）时间。
英文摘要：
We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show that the problem hardness is mainly due to entropic barriers. We study, both analytically and numerically, several optimization algorithms, finding that entropic barriers affect in a similar way classical local algorithms and quantum annealing. For the adiabatic algorithm, the difficulty we identify is distinct from that of tunnelling under large barriers, but does, nonetheless, give rise to exponential running (annealing) times.
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